Centralizer theory for long-lived spin states

Hyperpolarisation criteria in magnetic resonance

Nuclear Magnetic Resonance (NMR) techniques display an inherently low sensitivity due to a small equilibrium magnetisation. Nowadays this issue is easily overcome through the use of hyperpolarisation methods. This however raises the question as to what precisely do we mean by "hyperpolarisation". Recently a formal definition of hyperpolarisation has been given based on the von Neumann entropy of a system. Ideally this definition should conform with the general usage in the magnetic resonance community, where hyperpolarisation is often used synonymously with "larger" NMR signals. Within this article I show that an entropy-based hyperpolarisation criterion does not always conform with the general usage. Based on this observation I introduce an alternative hyperpolarisation criterion utilising the concept of latent polarisation, where latent polarisation is a measure of the highest possible amount of polarisation that may be extracted from a system. I show that a hyperpolarisation criterion based on latent polarisation correlates more strongly with the general usage within the magnetic resonance community. Ultimately however our results show that there are several possible notions of hyperpolarisation, and the choice depends upon the questions of interest.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.